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\title{Elliptic Curves over $\Q(\sqrt{5})$}

\author{Jon Bober, Alyson Deines, Joanna Gaski, Ariah Klages-Mundt,
Ben LeVeque,\\Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, 
William Stein\footnote{The work was supported by NSF 
grants (mainly the FRG)...}\footnote{This is a {\em long} list of authors for a math
paper.  Anybody who for some reason does not feel comfortable
being a co-author, e.g., would rather be moved to acknowledgements, please let William know.}}

\begin{document}
\maketitle

\begin{abstract} 
\end{abstract}

% useful when working on the paper -- remove for publication, probably.
\tableofcontents

\section{Introduction}\label{sec:intro}

Introduction and overview goes here.

\noindent{\bf Acknowledgement: } Richard Taylor, Rado Kirov. 

\section{Sorting and Labeling Curves}\label{sec:sort}
    \input{sorting.tex}

\section{Computing Hilbert Modular Forms}\label{sec:hmf}
    \input{hmf.tex}

\section{Finding Curves Associated to Hilbert Modular Forms}\label{sec:finding}
 
\subsection{Naive Search}

\subsection{Naive Search over Curves with Given $a_p$}
    \input{search_methods/mod_jon.tex}

\subsection{Integral Points (Cremona-Lingham)}
    \input{search_methods/Cremona_Lingham.tex}

\subsection{Torsion Families}
    \input{search_methods/torsion_families.tex}

\subsection{Using Special Values of $L$-functions and Periods}
    \input{search_methods/dembele.tex}


\section{Computing all Isogeny Classes}

\section{Saturating Mordell-Weil Groups}

\section{Computing $L$-series}

\section{Modularity}

(Statement of the conjecture.  Evidence we give.   What is known in this case (see email from Richard Taylor).)

\section{Table 1: Curves with Norm Conductor up to $1000$}


The actual tables will be sideways (landscape).... and depending on
length maybe in another document.  This might just be a discussion of
the tables.

\section{Table 2: Mordell-Weil Generators}

\section{Table 3: Hecke Eigenvalues}

\section{Table 4: Birch and Swinnerton-Dyer Data}

\section{Table 5: Parametrization Degrees}

(We will remove this section if nobody finds an algorithm to compute
these.  I don't know if there is an algorithm.  Note that one
complication is that there is a different parameterization
corresponding to each prime that exactly divides the level, and there
is no parameteriziation in some cases, e.g., when the level is a
perfect square.)



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